Volume 35, Issue 3
Stochastic Averaging Principle for Mixed Stochastic Differential Equations

J. Part. Diff. Eq., 35 (2022), pp. 223-239.

Published online: 2022-06

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• Abstract

In this paper, an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion, a fractional Brownian motion $B^{H}$ with the Hurst parameter $H>\frac{1}{2}$ and a discontinuous drift was estimated. Under some proper assumptions, we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the It$\hat{\mathrm{o}}$ stochastic calculus.

• Keywords

Averaging principle mixed stochastic differential equation discontinuous drift fractional Brownian motion.

26A42, 26A33, 60H05

lizhi_csu@126.com (Zhi Li)

15303412095@163.com (Yarong Peng)

jingyy120920@163.com (Yuanyuan Jing)

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@Article{JPDE-35-223, author = {Zhi and Li and lizhi_csu@126.com and 16537 and School of Information and Mathematics, Yangtze University, Jingzhou 434023, China and Zhi Li and Yarong and Peng and 15303412095@163.com and 23978 and School of Information and Mathematics, Yangtze University, Jingzhou 434023, China and Yarong Peng and Yuanyuan and Jing and jingyy120920@163.com and 10070 and School of Information and Mathematics, Yangtze University, Jingzhou 434023, China. and Yuanyuan Jing}, title = {Stochastic Averaging Principle for Mixed Stochastic Differential Equations}, journal = {Journal of Partial Differential Equations}, year = {2022}, volume = {35}, number = {3}, pages = {223--239}, abstract = {

In this paper, an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion, a fractional Brownian motion $B^{H}$ with the Hurst parameter $H>\frac{1}{2}$ and a discontinuous drift was estimated. Under some proper assumptions, we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the It$\hat{\mathrm{o}}$ stochastic calculus.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v35.n3.3}, url = {http://global-sci.org/intro/article_detail/jpde/20773.html} }
TY - JOUR T1 - Stochastic Averaging Principle for Mixed Stochastic Differential Equations AU - Li , Zhi AU - Peng , Yarong AU - Jing , Yuanyuan JO - Journal of Partial Differential Equations VL - 3 SP - 223 EP - 239 PY - 2022 DA - 2022/06 SN - 35 DO - http://doi.org/10.4208/jpde.v35.n3.3 UR - https://global-sci.org/intro/article_detail/jpde/20773.html KW - Averaging principle KW - mixed stochastic differential equation KW - discontinuous drift KW - fractional Brownian motion. AB -

In this paper, an averaging principle for the solutions to mixed stochastic differential equation involving standard Brownian motion, a fractional Brownian motion $B^{H}$ with the Hurst parameter $H>\frac{1}{2}$ and a discontinuous drift was estimated. Under some proper assumptions, we proved that the solutions of the simplified systems can be approximated to that of the original systems in the sense of mean square by the method of the pathwise approach and the It$\hat{\mathrm{o}}$ stochastic calculus.

Zhi Li, Yarong Peng & Yuanyuan Jing. (2022). Stochastic Averaging Principle for Mixed Stochastic Differential Equations. Journal of Partial Differential Equations. 35 (3). 223-239. doi:10.4208/jpde.v35.n3.3
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